Effects of aeroelasticity on coning motion of a spinning missile

The coning motion is a basic angular behavior of spinning missiles. Research on the stability of coning motion is always active. In this paper, the integrated nonlinear governing equations of rigid-elastic angular motion for a spinning missile with high fineness ratio are derived firstly following the Lagrangian approach. Secondly, a set of linear equation is obtained under some assumptions considering the first order vibration mode in the form of complex summation for theoretical analysis. Finally, the sufficient and necessary conditions of coning motion dynamic stability for spinning missile with and without an acceleration autopilot are analytically derived and verified by numerical simulations based on the linear equation. It is concluded that the aeroelasticity can shrink the stable region of the design parameters, even lead to a divergent coning motion.